JP Journal of Algebra, Number Theory and Applications
Volume 15, Issue 1, Pages 1 - 17
(October 2009)
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CONGRUENCE SUBGROUPS OF THE MODULAR GROUP RELATED TO CONGRUENCE RESTRICTIONS OF MODULAR FORMS
M. I. Knopp (U.S.A.) and Y. Omer (U.S.A.)
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of the
modular group. These subgroups arise naturally from the survival of modularity
under congruence restrictions of modular forms. In addition, we will show that
the index of these subgroups in the modular group is multiplicative and we will
reveal its connection with the number of inequivalent solutions to the quadratic
congruence